Mathematical Physics Seminar
Seminar given by Ramon van Handel and Ian Jauslin
Date & time: Thursday, 22 September 2016 at 12:00PM - 3:00PM
MATHEMATICAL PHYSICS SEMINAR
Ramon van Handel - Princeton University
Thursday, September 22nd, 12:00pm; Hill 705
"A Gaussian Gibbs variational principle and geometric inequalities"
The Gibbs variational principle has been a cornerstone of statistical mechanics since at least J. W. Gibbs' seminal 1902 treatise. It has also proved to be remarkably useful in other areas of mathematics, such as in the study of geometric inequalities of Brunn-Minkowski and Brascamp-Lieb type. This fundamental connection, pioneered by C. Borell, is however not sufficiently powerful to obtain the sharp isoperimetric and Brunn-Minkowski inequalities for Gaussian measures. In this talk, I will describe an unexpected Gaussian refinement of the Gibbs variational principle that makes it possible to recover these sharp inequalities. I will aim to explain how this gives rise to new Gaussian inequalities---in particular, a Gaussian improvement of Barthe's reverse Brascamp-Lieb inequality---and why the apparent duality between the Prekopa-Leindler and Holder inequalities is manifestly absent in the Gaussian setting.
THERE WILL BE A BROWN BAG LUNCH FROM 1-2PM. PLEASE JOIN US
Ian Jauslin - University of Rome
Thursday, September 22nd, 2:00pm; Hill 705
"Emergence of a nematic phase in a system of hard plates in three dimensions with discrete orientations."
We consider a system of hard parallelepipedes, which we call plates, of size 1 by k^a by k in which a is larger than 5/6 and no larger than 1. Each plate is in one of six orthogonal allowed orientations. We prove that, when the density of plates is sufficiently larger than k^(2-5a) and sufficiently smaller than k^(3-a), the rotational symmetry of the system is broken, but its translational invariance is not. In other words, the system is in a nematic phase. The argument is based on a two-scale cluster expansion, and uses ideas from the Pirogov-Sinai construction.